Question

What is the common ratio between successive terms in the sequence? 27, 9, 3, 1, , , , ...

Answer 1

Answer:

$Common\:ratio(r)=\frac{1}{3}$

Step-by-step explanation:

$Given \: sequence \:27,9,3,1,...$

$i) \frac{a_{2}}{a_{1}}\\=\frac{9}{27}\\=\frac{1}{3}$

$ii) \frac{a_{3}}{a_{2}}\\=\frac{3}{9}\\=\frac{1}{3}$

$iii) \frac{a_{4}}{a_{3}}\\=\frac{1}{3}$

$Here,\\\frac{a_{2}}{a_{1}}=\frac{a_{3}}{a_{2}}=\frac{a_{4}}{a_{3}}=\frac{1}{3}$

$Common\:ratio(r)=\frac{a_{n}}{a_{n-1}}=\frac{1}{3}$

Given Sequence is in Geometric progression.

Therefore,

$Common\:ratio(r)=\frac{1}{3}$

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